Simplify (z^(4/3))^(9/2)

Problem

(z(4/3))(9/2)

Solution

1. Apply the power of a power rule, which states that (am)n=a(m⋅n)

2. Multiply the exponents by calculating the product of the two fractions.

4/3⋅9/2

3. Simplify the fraction by dividing the numerator and denominator by their common factors.

(4⋅9)/(3⋅2)=36/6

4. Divide the terms to find the final exponent.

36/6=6

Final Answer

(z(4/3))(9/2)=z6

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